Molecular biology is becoming a computationally intense realm of conte
mporary science and faces some of the current grand scientific challen
ges. In its context, tools that identify, store, compare and analyze e
ffectively large and growing numbers of bio-sequences are found of inc
reasingly crucial importance. Biosequences are routinely compared or a
ligned, in a variety of ways, to infer common ancestry, to detect func
tional equivalence, or simply while searching for similar entries in a
database. A considerable body of knowledge has accumulated on sequenc
e alignment during the past few decades. Without pretending to be exha
ustive, this paper attempts a survey of some criteria of wide use in s
equence alignment and comparison problems, and of the corresponding so
lutions. The paper is based on presentations and literature given at t
he Workshop on Sequence Alignment held at Princeton, N,J,, in November
1994, as part of the DIMACS Special Year on Mathematical Support for
Molecular Biology.